First, let's define what an adverb does. An adverb is a word that modifies (describes or gives more information about) one of three things:
Adverbs typically answer questions like:
How? (e.g., slowly, carefully, quickly)
When? (e.g., now, yesterday, later)
Where? (e.g., here, outside, everywhere)
To what extent? (e.g., very, extremely, too)
Sentence: "She runs quickly to catch the bus."
Identify the Verb: The main action in the sentence is the verb runs.
Ask the "How?" Question: How does she run? The answer is quickly. Since "quickly" answers the question "how?" about the verb "runs," it is functioning as an adverb. It describes the manner in which the action is performed. It's not describing "she" (the subject), but rather the action of running.
Many adverbs, especially those that describe how an action is done (adverbs of manner), are formed by adding -ly to an adjective.
Other examples of this pattern include:
slow (adjective) -> slowly (adverb)
loud (adjective) -> loudly (adverb)
* careful (adjective) -> carefully (adverb)
To fully understand the role of "quickly" as an adverb, it helps to contrast it with its adjective form, "quick."
Adverb Example: "She runs quickly."
Here, quickly modifies the verb runs*. It describes the action.
Adjective Example: "She is a quick runner."
Here, quick modifies the noun runner*. It describes the person, not the action.
In summary, "quickly" is an adverb in your sentence because it directly modifies the verb "runs" by explaining how the action is being performed.